Exploration seismology is a field of study that concentrates on how to construct an image of the Earth's subsurface using measurements of seismic waves at the Earth's surface. The premise of image construction is that if we understand how seismic waves propagate in the Earth, we can computationally project the recorded waves back into an Earth model, and accumulate the projected waves into an image. The projection process is referred to as seismic migration. The accumulation process is referred to as diffraction stacking, but in the present invention it has been recognized that it can be split into two steps: one is conventionally referred to as “stacking” and the other may be referred to as “assembly”. At locations where a subsurface object scattered the waves, the contributions from many measurements align by migration and constructively interfere by summation, thereby revealing the real locations of scattering objects. Contributions that are thought to be redundant constructively interfere by stacking, while contributions that are thought to be neighboring constructively interfere by assembly. The performance of the image construction process relies on how accurately the projection itself can be performed, and how well the subsurface model can be predicted, yet both factors even in the state-of-the-art have known deficiencies. Under the conventional imaging approach, migration, assembly, and most of stacking are performed together. Migration places redundant and neighboring contributions close to each other in the image space, yet if imaging deficiencies remain, the signals will not be aligned for optimum interference during summation, and premature summation prevents the measurement and compensation of many imaging deficiencies. The present invention addresses these deficiencies by completely separating the steps of migration and summation. By storing all individual contributing signals after migration, remaining imaging deficiencies can be measured and addressed in the image space before they are obscured by summation. Afterward, summation proceeds to construct the final image.
Partial separation of migration and stacking is common practice through the use of so-called “image gathers”, but in this approach, image assembly is performed simultaneously with migration. The present invention fully separates the steps of migration, assembly, and stacking. The product of the present inventive method may be referred to as an “expanded image-gather” (EIG). Conventional image gathers allow the measurement of only velocity-related imaging deficiencies post-migration, whereas the present invention can be used to capture far more deficiencies. A representative reference for conventional image gathers is Sava and Fomel, “Angle-domain common-image gathers by wavefield continuation methods,” Geophysics 68, 1065-1074 (2003).
A three-dimensional extension of the image gather, called “offset-vector tiling” (OVT) or “common offset-vector” (COV) gathering, is known in the literature. This type of image gather is designed to capture imaging deficiencies related to azimuthal variation in seismic velocity. OVT and COV gathers cannot address imaging deficiencies of other types, as migration and assembly are still performed together. In the 2D case, OVT and COV gathers each collapse to a conventional image gather, while the “expanded image gather” of the present invention remains expanded over the additional dimension required to keep migration and assembly separate. A representative reference for OVT and COV gathers is: Cary, “Common-offset-vector gathers: an alternative to cross-spreads for wide-azimuth 3-D surveys,” Expanded Abstracts of the 69th Annual Meeting of the Society of Exploration Geophysicists, 1496-1499 (1999).
A sub-class of existing image-gather technology is the so-called “dip-angle gather”. A key difference between dip-angle gathers and the expanded image-gathers of the present invention comes from the physics built-in to the gather formation. During dip-angle-gather formation, geometrical calculations are made to predict and then collect image contributions based on a range of possible scattering and reflector dip angles. The expanded image-gathers of the present invention are formed with no assumptions regarding scatter or dip angle. A representative reference on dip-angle gathers is: Koren and Ravve, “Full-azimuth subsurface angle domain wavefield decomposition and imaging Part I: Directional and reflection image gathers,” Geophysics 76, S1-S13 (2011).
A particular example of the dip-angle-gather approach is that of Kabbej et al., “Aperture optimized two-pass Kirchhoff migration,” Expanded Abstracts of the 77th Annual Meeting of the Society of Exploration Geophysicists, 2339-2343 (2007). The “expanded” axis of the present invention is most simply thought of as acquisition midpoint, but it might possibly be construed to have some sort of geometrical equivalence to the midpoint-to-image-point dimension Kabbej and his co-authors introduce as “deport”. However, they do not produce images using this extra dimension; they simply map a sparse subset of the data to this domain in order to estimate a well-known parameter called migration aperture, and then use the aperture to perform conventional migration. The present inventive method constructs images directly from the “offset-midpoint” (or “offset-deport”) domain, and also permits processing in this domain.